Time dependent numerical model for the emission of radiation from relativistic plasma

We describe a numerical model constructed for the study of the emission of radiation from relativistic plasma under conditions characteristic, e.g., to gamma-ray bursts (GRB's) and active galactic nuclei (AGN's). The model solves self consistently the kinetic equations for e^\pm and photons, describing cyclo-synchrotron emission, direct Compton and inverse Compton scattering, pair production and annihilation, including the evolution of high energy electromagnetic cascades. The code allows calculations over a wide range of particle energies, spanning more than 15 orders of magnitude in energy and time scales. Our unique algorithm, which enables to follow the particle distributions over a wide energy range, allows to accurately derive spectra at high energies, >100 \TeV. We present the kinetic equations that are being solved, detailed description of the equations describing the various physical processes, the solution method, and several examples of numerical results. Excellent agreement with analytical results of the synchrotron-SSC model is found for parameter space regions in which this approximation is valid, and several examples are presented of calculations for parameter space regions where analytic results are not available.